An approach to higher order linking invariants through holonomy and curvature (Q2841354)

For a link, the Milnor invariants are defined by considering the Magnus expansions of the images of longitudes in the quotient of the link group by lower central series subgroups. There is an interpretation of Milnor invariants in terms of Massey products by \textit{V. G. Turaev} [Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 66, 189--203 (1976; Zbl 0354.55013); English transl. in J. Sov. Math. 12, 128--137 (1979; Zbl 0406.55017)] and \textit{R. Porter} [Trans. Am. Math. Soc. 257, 39--71 (1980; Zbl 0423.57005)].NEWLINENEWLINEThe paper under review uses ideas from the work of \textit{V. Penna} and \textit{M. Spera} [J. Knot Theory Ramifications 11, No. 5, 701--723 (2002; Zbl 1027.57007)] and gives a relation between Milnor invariants, Massey products and the holonomy and curvature of certain nilpotent connections. However, the last part gives a counterexample to two theorems in this work.